{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Lotka-Volterra Colab",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "v9inRWqjA_aw"
      },
      "source": [
        "pip install deepxde"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OgtisP9zBSCF"
      },
      "source": [
        "#approximate upper bound of range\r\n",
        "#right bound of domain (used for scaling)\r\n",
        "\r\n",
        "ub = 200\r\n",
        "rb = 20"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "4EVKhzoSBDlL",
        "outputId": "135d9c3a-0fd3-42cb-f126-bd54f047b377"
      },
      "source": [
        "from __future__ import absolute_import\r\n",
        "from __future__ import division\r\n",
        "from __future__ import print_function\r\n",
        "import math\r\n",
        "from deepxde.backend import tf\r\n",
        "import numpy as np\r\n",
        "import matplotlib.pyplot as plt\r\n",
        "\r\n",
        "import deepxde as dde\r\n",
        "\r\n",
        "\r\n",
        "def ode_system(x, y):\r\n",
        "    r = y[:, 0:1]\r\n",
        "    p = y[:, 1:2]\r\n",
        "    dr_t = dde.grad.jacobian(y, x, i=0)\r\n",
        "    dp_t = dde.grad.jacobian(y, x, i=1)\r\n",
        "    return [\r\n",
        "        dr_t - 1 / ub * rb * (2.0 * ub * r - 0.04 * ub * r * ub * p),\r\n",
        "        dp_t - 1 / ub * rb * (0.02 * r * ub * p * ub - 1.06 * p * ub),\r\n",
        "    ]\r\n",
        "\r\n",
        "\r\n",
        "def boundary(_, on_initial):\r\n",
        "    return on_initial\r\n",
        "\r\n",
        "\r\n",
        "geom = dde.geometry.TimeDomain(0.0, 1.0)\r\n",
        "data = dde.data.PDE(geom, ode_system, [], 3000, 2, num_test=3000)\r\n",
        "\r\n",
        "layer_size = [1] + [64] * 6 + [2]\r\n",
        "activation = \"tanh\"\r\n",
        "initializer = \"Glorot normal\"\r\n",
        "net = dde.maps.FNN(layer_size, activation, initializer)\r\n",
        "\r\n",
        "\r\n",
        "def input_transform(t):\r\n",
        "    return tf.concat(\r\n",
        "        (\r\n",
        "            t,\r\n",
        "            tf.sin(t),\r\n",
        "            tf.sin(2 * t),\r\n",
        "            tf.sin(3 * t),\r\n",
        "            tf.sin(4 * t),\r\n",
        "            tf.sin(5 * t),\r\n",
        "            tf.sin(6 * t),\r\n",
        "        ),\r\n",
        "        axis=1,\r\n",
        "    )\r\n",
        "\r\n",
        "\r\n",
        "# hard constraints: x(0) = 100, y(0) = 15\r\n",
        "def output_transform(t, y):\r\n",
        "    y1 = y[:, 0:1]\r\n",
        "    y2 = y[:, 1:2]\r\n",
        "\r\n",
        "    return tf.concat(\r\n",
        "        (y1 * tf.math.tanh(t) + 100 / ub, y2 * tf.math.tanh(t) + 15 / ub), axis=1\r\n",
        "    )\r\n",
        "\r\n",
        "\r\n",
        "net.apply_feature_transform(input_transform)\r\n",
        "net.apply_output_transform(output_transform)\r\n",
        "\r\n",
        "model = dde.Model(data, net)\r\n",
        "model.compile(\"adam\", lr=0.001)\r\n",
        "losshistory, train_state = model.train(epochs=50000)\r\n",
        "\r\n",
        "model.compile(\"L-BFGS-B\")\r\n",
        "losshistory, train_state = model.train()\r\n",
        "\r\n",
        "dde.saveplot(losshistory, train_state, issave=True, isplot=True)\r\n"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Compiling model...\n",
            "Building feed-forward neural network...\n",
            "'build' took 0.109589 s\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/legacy_tf_layers/core.py:171: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n",
            "  warnings.warn('`tf.layers.dense` is deprecated and '\n",
            "/usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/engine/base_layer_v1.py:1719: UserWarning: `layer.apply` is deprecated and will be removed in a future version. Please use `layer.__call__` method instead.\n",
            "  warnings.warn('`layer.apply` is deprecated and '\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "'compile' took 1.312164 s\n",
            "\n",
            "Initializing variables...\n",
            "Training model...\n",
            "\n",
            "Step      Train loss              Test loss               Test metric\n",
            "0         [2.50e+03, 9.50e+01]    [2.50e+03, 9.49e+01]    []  \n",
            "1000      [3.88e+00, 5.07e-01]    [3.93e+00, 5.08e-01]    []  \n",
            "2000      [9.51e+00, 1.94e-01]    [9.59e+00, 1.93e-01]    []  \n",
            "3000      [6.61e+00, 2.76e-01]    [6.68e+00, 2.75e-01]    []  \n",
            "4000      [5.08e+00, 3.09e-01]    [5.15e+00, 3.08e-01]    []  \n",
            "5000      [3.97e+00, 4.44e-01]    [4.03e+00, 4.45e-01]    []  \n",
            "6000      [3.19e+00, 5.65e-01]    [3.25e+00, 5.66e-01]    []  \n",
            "7000      [2.57e+00, 6.19e-01]    [2.62e+00, 6.22e-01]    []  \n",
            "8000      [1.97e+00, 6.51e-01]    [2.01e+00, 6.54e-01]    []  \n",
            "9000      [1.45e+00, 5.95e-01]    [1.48e+00, 5.99e-01]    []  \n",
            "10000     [1.01e+00, 4.47e-01]    [1.04e+00, 4.51e-01]    []  \n",
            "11000     [7.03e-01, 3.55e-01]    [7.19e-01, 3.58e-01]    []  \n",
            "12000     [4.97e-01, 3.07e-01]    [5.09e-01, 3.10e-01]    []  \n",
            "13000     [3.26e-01, 2.58e-01]    [3.33e-01, 2.61e-01]    []  \n",
            "14000     [2.18e-01, 2.11e-01]    [2.22e-01, 2.14e-01]    []  \n",
            "15000     [1.43e-01, 1.78e-01]    [1.45e-01, 1.80e-01]    []  \n",
            "16000     [1.47e-01, 1.40e-01]    [1.47e-01, 1.42e-01]    []  \n",
            "17000     [8.06e-02, 1.07e-01]    [8.05e-02, 1.08e-01]    []  \n",
            "18000     [5.33e-02, 8.72e-02]    [5.32e-02, 8.77e-02]    []  \n",
            "19000     [4.53e-02, 7.06e-02]    [4.52e-02, 7.07e-02]    []  \n",
            "20000     [4.07e-02, 1.00e-01]    [4.07e-02, 1.00e-01]    []  \n",
            "21000     [2.64e-02, 4.16e-02]    [2.63e-02, 4.16e-02]    []  \n",
            "22000     [2.13e-02, 3.19e-02]    [2.13e-02, 3.19e-02]    []  \n",
            "23000     [2.12e-02, 2.26e-02]    [2.12e-02, 2.26e-02]    []  \n",
            "24000     [1.84e-02, 2.44e-02]    [1.83e-02, 2.44e-02]    []  \n",
            "25000     [1.01e-02, 1.26e-02]    [1.01e-02, 1.26e-02]    []  \n",
            "26000     [9.83e-03, 1.23e-02]    [9.81e-03, 1.23e-02]    []  \n",
            "27000     [2.52e-02, 9.38e-03]    [2.52e-02, 9.38e-03]    []  \n",
            "28000     [3.34e-02, 1.36e-02]    [3.34e-02, 1.36e-02]    []  \n",
            "29000     [1.49e-02, 9.46e-03]    [1.48e-02, 9.45e-03]    []  \n",
            "30000     [5.78e-03, 7.17e-03]    [5.77e-03, 7.17e-03]    []  \n",
            "31000     [9.69e-03, 7.25e-03]    [9.68e-03, 7.24e-03]    []  \n",
            "32000     [4.65e-03, 5.25e-03]    [4.65e-03, 5.25e-03]    []  \n",
            "33000     [4.72e-02, 1.03e-02]    [4.72e-02, 1.03e-02]    []  \n",
            "34000     [4.08e-03, 4.86e-03]    [4.08e-03, 4.86e-03]    []  \n",
            "35000     [1.71e-01, 1.93e-02]    [1.71e-01, 1.93e-02]    []  \n",
            "36000     [3.58e-03, 3.81e-03]    [3.58e-03, 3.81e-03]    []  \n",
            "37000     [5.49e-03, 6.20e-03]    [5.48e-03, 6.20e-03]    []  \n",
            "38000     [2.57e-02, 2.70e-02]    [2.57e-02, 2.69e-02]    []  \n",
            "39000     [2.70e-03, 2.67e-03]    [2.70e-03, 2.67e-03]    []  \n",
            "40000     [2.91e-03, 2.44e-03]    [2.91e-03, 2.44e-03]    []  \n",
            "41000     [2.65e-03, 2.65e-03]    [2.65e-03, 2.65e-03]    []  \n",
            "42000     [2.25e-03, 2.17e-03]    [2.25e-03, 2.17e-03]    []  \n",
            "43000     [2.63e-03, 2.43e-03]    [2.62e-03, 2.43e-03]    []  \n",
            "44000     [2.22e-03, 2.32e-03]    [2.21e-03, 2.32e-03]    []  \n",
            "45000     [2.85e-03, 2.34e-03]    [2.84e-03, 2.34e-03]    []  \n",
            "46000     [2.47e-02, 5.30e-03]    [2.47e-02, 5.30e-03]    []  \n",
            "47000     [8.29e-03, 2.38e-03]    [8.29e-03, 2.38e-03]    []  \n",
            "48000     [1.80e-03, 1.77e-03]    [1.80e-03, 1.77e-03]    []  \n",
            "49000     [1.61e-03, 1.72e-03]    [1.61e-03, 1.72e-03]    []  \n",
            "50000     [2.61e-02, 2.88e-02]    [2.61e-02, 2.89e-02]    []  \n",
            "\n",
            "Best model at step 49000:\n",
            "  train loss: 3.33e-03\n",
            "  test loss: 3.33e-03\n",
            "  test metric: []\n",
            "\n",
            "'train' took 383.299785 s\n",
            "\n",
            "Compiling model...\n",
            "'compile' took 0.817922 s\n",
            "\n",
            "Training model...\n",
            "\n",
            "Step      Train loss              Test loss               Test metric\n",
            "50000     [2.61e-02, 2.88e-02]    [2.61e-02, 2.89e-02]    []  \n",
            "51000     [6.28e-05, 5.05e-05]                                \n",
            "52000     [1.94e-05, 2.04e-05]                                \n",
            "53000     [9.30e-06, 1.01e-05]                                \n",
            "INFO:tensorflow:Optimization terminated with:\n",
            "  Message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
            "  Objective function value: 0.000014\n",
            "  Number of iterations: 3407\n",
            "  Number of functions evaluations: 3751\n",
            "53751     [6.51e-06, 7.63e-06]    [6.52e-06, 7.73e-06]    []  \n",
            "\n",
            "Best model at step 53751:\n",
            "  train loss: 1.41e-05\n",
            "  test loss: 1.42e-05\n",
            "  test metric: []\n",
            "\n",
            "'train' took 159.524235 s\n",
            "\n",
            "Saving loss history to loss.dat ...\n",
            "Saving training data to train.dat ...\n",
            "Saving test data to test.dat ...\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 364
        },
        "id": "PaIahCF0D1mV",
        "outputId": "64f8ea35-ad09-4d93-ce32-111d4871c40b"
      },
      "source": [
        "from scipy import integrate\r\n",
        "import numpy as np\r\n",
        "import matplotlib.pyplot as plt\r\n",
        "\r\n",
        "\r\n",
        "def func(t, r):\r\n",
        "    x, y = r\r\n",
        "    dx_t = 1 / ub * rb * (2.0 * ub * x - 0.04 * ub * x * ub * y)\r\n",
        "    dy_t = 1 / ub * rb * (0.02 * ub * x * ub * y - 1.06 * ub * y)\r\n",
        "    return dx_t, dy_t\r\n",
        "\r\n",
        "\r\n",
        "t = np.linspace(0, 1, 100)\r\n",
        "\r\n",
        "sol = integrate.solve_ivp(func, (0, 10), (100 / ub, 15 / ub), t_eval=t)\r\n",
        "x_true, y_true = sol.y\r\n",
        "x_true = x_true.reshape(100, 1)\r\n",
        "y_true = y_true.reshape(100, 1)\r\n",
        "plt.plot(t, x_true, color=\"black\", label=\"x_true\")\r\n",
        "plt.plot(t, y_true, color=\"blue\", label=\"y_true\")\r\n",
        "\r\n",
        "t = t.reshape(100, 1)\r\n",
        "sol_pred = model.predict(t)\r\n",
        "x_pred = sol_pred[:, 0:1]\r\n",
        "y_pred = sol_pred[:, 1:2]\r\n",
        "\r\n",
        "plt.xlabel(\"t\")\r\n",
        "plt.ylabel(\"population\")\r\n",
        "plt.plot(t, x_pred, color=\"red\", linestyle=\"dashed\", label=\"x_pred\")\r\n",
        "plt.plot(t, y_pred, color=\"orange\", linestyle=\"dashed\", label=\"y_pred\")\r\n",
        "plt.legend()\r\n",
        "plt.show()\r\n",
        "\r\n",
        "\r\n",
        "print(\"L2 relative error for x:\", dde.metrics.l2_relative_error(x_true, x_pred))\r\n",
        "print(\"L2 relative error for y:\", dde.metrics.l2_relative_error(y_true, y_pred))\r\n"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Predicting...\n",
            "'predict' took 0.004915 s\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "L2 relative error for x: 0.0811613401704079\n",
            "L2 relative error for y: 0.055192571364509814\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}
